The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.
A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.
1) What is the capability score of the supplier?
2) What percentage of the deliveries is likely to be outside the specification limits (outside the interval of [94.5, 95.5])?
3) To what level would the supplier have to reduce the standard deviation of the operation if his goal were to obtain a capability score of 1 (i.e., get less than or equal to 0.27 percent defective)?
(Note: Please enter your answer as a decimal. Fractions are not accepted by the software)